Let H be the real algebra of quaternions. The notion of regular function of a quaternionic variable recently presented by G. Gentili and D. C. Struppa developed into a quite rich theory. Several properties of regular quaternionic functions are analogous to those of holomorphic functions of one complex variable, although the diversity of the quaternionic setting introduces new phenomena. This pa...

The existing classification of homogeneous quaternionic spaces is not complete. We study these spaces in the context of certain N = 2 supergravity theories, where dimensional reduction induces a mapping between special real, Kähler and quaternionic spaces. The geometry of the real spaces is encoded in cubic polynomials, those of the Kähler and quaternionic manifolds in homogeneous holomorphic f...

We prove that a compact quaternionic-Kähler manifold of dimension 4n ≥ 8 admitting a conformal-Killing 2-form which is not Killing, is isomorphic to the quaternionic projective space, with its standard quaternionicKähler structure.

We remind known and establish new properties of the Dieudonné and Moore determinants of quaternionic matrices. Using these linear algebraic results we develop a basic theory of plurisubharmonic functions of quaternionic variables.

A suitable parameterization of space-time in terms of one complex and three quaternionic imaginary units allows Lorentz transformations to be implemented as multiplication by complex-quaternionic numbers rather than matrices. Maxwell’s equations reduce to a single equation.

In this article, we establish a sharp inequality involving δ-invariant introduced by Chen for submanifolds in quaternionic space forms of constant quaternionic sectional curvature with arbitrary codimension. Mathematics Subject Classification: 53B25, 53B35.

The purpose of this paper is to locate and estimate the left eigenvalues of quaternionic matrices. We present some distribution theorems for the left eigenvalues of square quaternionic matrices based on the generalized Gerschgorin theorem and generalized Brauer theorem.

In this note we prove that if the fundamental 4-form of an almost-quaternionic Hermitian manifold (M,Q, g) of dimension 4n ≥ 8 satisfies the conformal-Killing equation, then (M,Q, g) is quaternionic-Kähler.

Hilbert Huang Transform is a new developed method for signal processing especially suitable for non-stationary signal processing. In this paper, we propose a two dimensional Hilbert-Huang Transform based on Bidimensional Empirical Mode Decomposition (BEMD) and quaternionic analytic signal. Bidimensional Empirical Mode Decomposition is adaptive signal decomposition method and its decomposition r...

We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two altern...